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Choose the correct option from the followingQuantity I: If A and B can do a piece of work in 10 days, B and C in 12 days and if all three are together then said work is done in 8 days. In how many days would C and A complete the work if working together?Quantity II: A can do a piece of work in 2/5th of work in 10 days and B can do 1/2 of the same work in 8 days. If both of them are working together then in how many days would the work get completed?1. Quantity I ≥ Quantity II2. Quantity I ≤ Quantity II3. Quantity I < Quantity II4. Quantity I = Quantity II5. Quantity I > Quantity II |
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Answer» Correct Answer - Option 5 : Quantity I > Quantity II Given: A + B = 10 days B + C = 12 days A + B + C = 8 days 2/5th of work by A = 10 days 1/2 of work by B = 8 days Solution: Quantity I : 2/ (A + B + C) = (1/(A + B)) + (1/(B + C)) + (1/C + A)) ⇒ 2/ 8 = (1/ 10) + (1/12) + (1/x) ⇒ 1/ X = 1/4 – ((1/10) + (1/12)) ⇒ 1/ X = 15/60 – (11/60) ⇒ 1/ X = 4/60 1/X = 1/15 ⇒ X = 15 days Quantity II : A completes whole work = 10 × 5/2 ⇒ A completes whole work = 25 B completes whole work = 16 (∵ 8 × 2 = 16) ⇒ 1/X = (1/25) + (1/16) ⇒ 1/X = 41/400 X = 400/41 = 9.75 days ∴ Quantity I > Quantity II |
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